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arXiv · 1604.06035

The validity of Whitham's approximation for a Klein-Gordon-Boussinesq model

Wolf-Patrick Düll·Kourosh Sanei Kashani·Guido Schneider
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Abstract

In this paper we prove the validity of a long wave Whitham approximation for a system consisting of a Boussinesq equation coupled with a Klein-Gordon equation. The proof is based on an infinite series of normal form transformations and an energy estimate. We expect that the concepts of this paper will be a part of a general approximation theory for Whitham's equations which are especially used in the description of slow modulations in time and space of periodic wave trains in general dispersive wave systems.

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Wolf-Patrick Düll, Kourosh Sanei Kashani, Guido Schneider. 2016-04-20. The validity of Whitham's approximation for a Klein-Gordon-Boussinesq model. https://doi.org/10.1137/16m1071687

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